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  • Integrated data envelopment analysis: Linear vs. nonlinear model

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    MahdilooPUB6459.pdf (1.327Mb)
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    Accepted Manuscript (AM)
    Author(s)
    Tatham, Peter
    Tooloo, M
    Mahdiloo, M
    Jafarzdeh, A
    Saen, R
    Griffith University Author(s)
    Duong, Thach-Thao Nguyen N.
    Tatham, Peter H.
    Mahdiloo, Mahdi
    Year published
    2018
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    Abstract
    This paper develops a relationship between two linear and nonlinear data envelopment analysis (DEA) models which have previously been developed for the joint measurement of the efficiency and effectiveness of decision making units (DMUs). It will be shown that a DMU is overall efficient by the nonlinear model if and only if it is overall efficient by the linear model. We will compare these two models and demonstrate that the linear model is an efficient alternative algorithm for the nonlinear model. We will also show that the linear model is more computationally efficient than the nonlinear model, it does not have the potential ...
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    This paper develops a relationship between two linear and nonlinear data envelopment analysis (DEA) models which have previously been developed for the joint measurement of the efficiency and effectiveness of decision making units (DMUs). It will be shown that a DMU is overall efficient by the nonlinear model if and only if it is overall efficient by the linear model. We will compare these two models and demonstrate that the linear model is an efficient alternative algorithm for the nonlinear model. We will also show that the linear model is more computationally efficient than the nonlinear model, it does not have the potential estimation error of the heuristic search procedure used in the nonlinear model, and it determines global optimum solutions rather than the local optimum. Using 11 different data sets from published papers and also 1000 simulated sets of data, we will explore and compare these two models. Using the data set that is most frequently used in the published papers, it is shown that the nonlinear model with a step size equal to 0.00001, requires running 1,955,573 linear programs (LPs) to measure the efficiency of 24 DMUs compared to only 24 LPs required for the linear model. Similarly, for a very small data set which consists of only 5 DMUs, the nonlinear model requires running 7861 LPs with step size equal to 0.0001, whereas the linear model needs just 5 LPs.
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    Journal Title
    European Journal of Operational Research
    Volume
    268
    Issue
    1
    DOI
    https://doi.org/10.1016/j.ejor.2018.01.008
    Copyright Statement
    © 2018 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence (http://creativecommons.org/licenses/by-nc-nd/4.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, providing that the work is properly cited.
    Subject
    Business systems in context
    Human resources and industrial relations
    Strategy, management and organisational behaviour
    International business
    Publication URI
    http://hdl.handle.net/10072/380078
    Collection
    • Journal articles

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